A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?
A) 60(x-C) / 60+ m
B) x - C / m
C) 60(x-m) / C
D) m / 60(x-C)
E) 60(x-C)/ m
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Computer operator question
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theCEO
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wayne0426 wrote:A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?
A) 60(x-C) / 60+ m
B) x - C / m
C) 60(x-m) / C
D) m / 60(x-C)
E) 60(x-C)/ m
In 1hour, x mistakes are made
In (60+m)/60 hour, x-c mistakes are made
mistakes per hour= (x-c)/[(60+m)/60)
mistakes per hour= 60(x-c)/60+m
ans = a
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Let x=10, implying that 10 mistakes are made in the first hour.wayne0426 wrote:A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?
A) 60(x-C) / 60+ m
B) x - C / m
C) 60(x-m) / C
D) m / 60(x-C)
E) 60(x-C)/ m
Let C=0 and m=60 minutes, implying that 0 mistakes are corrected in the next hour.
Mistakes per hour = (total mistakes)/(total time) = (10 mistakes)/(2 hours) = 5. This is our target.
Now plug x=10, C=0 and m=60 into the answer choices to see which yields our target of 5.
Only A works:
60(x-C) / 60+ m = 60(10-0) / (60+60) = 5.
The correct answer is A.
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Matt@VeritasPrep
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Just to leave an algebraic explanation for posterity:
Our operator mworked for 1 + (m/60) hours.
In that time, she made x mistakes, then corrected C of them, leaving her with (x - C) total mistakes.
This gives us
Mistakes/Hours = (x - C) / (1 + (m/60))
= (x - C) / ((60 + m)/60)
= 60*(x - C) / (60 + m)
Our operator mworked for 1 + (m/60) hours.
In that time, she made x mistakes, then corrected C of them, leaving her with (x - C) total mistakes.
This gives us
Mistakes/Hours = (x - C) / (1 + (m/60))
= (x - C) / ((60 + m)/60)
= 60*(x - C) / (60 + m)
Hello @GMATGuruNY,
Thanks a ton for this approach. Need a small clarification though. The question says that x is greater than 30. Is this just a distraction? I see that in any case, we get the same answer.
Thanks in advance!
Thanks a ton for this approach. Need a small clarification though. The question says that x is greater than 30. Is this just a distraction? I see that in any case, we get the same answer.
Thanks in advance!
GMATGuruNY wrote:Let x=10, implying that 10 mistakes are made in the first hour.wayne0426 wrote:A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?
A) 60(x-C) / 60+ m
B) x - C / m
C) 60(x-m) / C
D) m / 60(x-C)
E) 60(x-C)/ m
Let C=0 and m=60 minutes, implying that 0 mistakes are corrected in the next hour.
Mistakes per hour = (total mistakes)/(total time) = (10 mistakes)/(2 hours) = 5. This is our target.
Now plug x=10, C=0 and m=60 into the answer choices to see which yields our target of 5.
Only A works:
60(x-C) / 60+ m = 60(10-0) / (60+60) = 5.
The correct answer is A.
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GMATGuruNY
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As my solution above illustrates, the constraint in red can be ignored.susheelh wrote:Hello @GMATGuruNY,
Thanks a ton for this approach. Need a small clarification though. The question says that x is greater than 30. Is this just a distraction? I see that in any case, we get the same answer.
Thanks in advance!
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As a tutor, I don't simply teach you how I would approach problems.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Scott@TargetTestPrep
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Since she corrected C mistakes, the number of her mistakes after correction is x - C and the time spent in total, typing and correcting mistakes, is 1 hour and m minutes, or 1 + m/60 hours. Thus, the number of mistakes she has made per hour is:wayne0426 wrote:A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?
A) 60(x-C) / 60+ m
B) x - C / m
C) 60(x-m) / C
D) m / 60(x-C)
E) 60(x-C)/ m
(x - C)/(1 + m/60) = 60(x - C)/(60 + m)
Answer: A
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